Pre-Algebra Sponsored by the Indiana Council of Teachers of Mathematics. Indiana State Mathematics Contest

Transcription

1 Pre-Algebra 2010 Sponsored by the Indiana Council of Teachers of Mathematics Indiana State Mathematics Contest This test was prepared by faculty at Indiana State University ICTM Website Do not open this test booklet until you have been advised by the test proctor. Next year s math contest date: April 23, 2011

2 1) is equal to E) ) is equal to E) 9 3) The integer closest to is E) 64 4) Of the following five numbers, 1.1, 1.01, 1.001, , , the one that is the least is E) ) Of the numbers , 0.9, 0.89, and 0.289, the sum of the smallest and the largest is E) ) The smallest number in the set {(-2.3) 2, 1.03, 4, (1.02) 2, (1.25) 2 } is (-2.3) (1.02) 2 E) (1.25) 2 Indiana State University Page 2 of 8 4/24/2010

3 7) ( 0.03) equals E) ) equals E) ) Of the following sets of angles, the one which could be the angles of an isosceles triangle is 40, 60, 80 91, 8, 91 70, 70, 70 50, 50, 70 E) 54, 72, 54 10) The number of degrees in one interior angle of a regular polygon is x. In terms of x, the number of sides of the polygon is 2x x x 360 x E) x 11) A triangle ABC is obtuse-angled at C. The bisectors of the exterior angle at A and B meet and at D and E respectively. If then the measure of is equal to E) none of these Indiana State University Page 3 of 8 4/24/2010

4 12) The lengths of the sides of a triangle are,, and. The number of values of b for which the triangle is isosceles is E) none of these 13) The average of 0.5, 2, and 0.75 is E) none of these 14) The average of 2 3, 0.7 and is E) ) The regular price of a pencil is 10 cents and a special sale price for Mondays is 5 cents. If Karen bought 15 pencils on Saturday and 10 on Monday, then how much did she pay for pencils? $50 $1.50 $2 $3 E) none of these 16) Of the following, the one which is not a natural number is E) Indiana State University Page 4 of 8 4/24/2010

5 17) The integer 119 is exactly divisible by E) none of these 18) The number of natural number divisors of 60, excluding 1 and 60, is E) 3 19) If,,, then the value of is E) none of these 20) If a, b, and c are real numbers such that, then the minimum value of is -1 0 E) 21) If and are the sides of a right-angled triangle, then the ratio is 4:1 8:1 20:21 20:1 E) none of these 22) The side, front, and bottom faces of a rectangular solid have areas of,, and square centimeters, respectively. The volume of the solid, in cubic centimeters is E) Cannot be determined from the information given. Indiana State University Page 5 of 8 4/24/2010

6 23) = E) ) The points A(30, 40), B(40, 30), C(-30, -40), D(30, -40), and E(40, -30) are marked on a coordinate grid. The line segment that is horizontal is E) 25) The point (400, -300) is reflected in the x-axis. The image is then reflected in the y-axis. The coordinates of the point in its final position are (300, -400) (-300, 400) (-400, 300) (-400, -300) E) (-300, -400) 26) If the point (10, 40) is reflected in the line, then its image is (30, 40) (-10, 40) (10,0) (10, -60) E) none of these 27) If the point is first reflected in the line, and the resulting point reflected in the line, the image is the point E) 28) If (2, 5) is the midpoint of the line segment joining (5, y) and (x, 7), then x + y is equal to E) none of these Indiana State University Page 6 of 8 4/24/2010

7 29) If and represent the same straight line, then equals E) 30) The ratio of boys to girls in a class is 2:3. If there are 30 students in the class, how many more girls than boys are in the class? E) none of these 31) If a and b are the x- and y- intercepts of a line which passes through the point (2, 1), then E) none of these 32) The lines,, and form a triangle. The number of points with integral coordinates which are inside this triangle is E) more than 3 33) If the area of the square is 36, then the area of the inscribed circle is E) Indiana State University Page 7 of 8 4/24/2010

8 34) The area of a given circle is 9π cm 2. The diameter of this circle, in cm, is E) 35) A number which is a multiple of 15, but not a multiple of 18 is: E) ) If you walk for 45 minutes at a rate of 4 mph and then run for 30 minutes at a rate of 10 mph, how many miles have you gone at the end of one hour and 15 minutes? E) none of these 37) The difference between a 7.5% sales tax and a 7% sales tax on an item priced at $200 before tax is: $0.10 $1.00 $5.00 $10.00 E) none of these 38) If a and b are two integers with b > a, then the number of integers between a and b is E) none of these 39) An unusual die has its six faces labeled 1, 2, 3, 5, 7, 9. If two such dice are rolled, and the numbers showing on the upper faces are added, then the number of possible different sums is E) 13 40) On each play in a game any one of 5, 4, 3, 2, or 0 points can be scored. The number of combinations of these scores which yield a total of 30 points in 7 plays is E) none of these Indiana State University Page 8 of 8 4/24/2010